Syllabus

1.Crystal structure

Periodic arrays of atoms: basis and the crystal structure, primitive lattice. Fundamental types of lattices: 2 and 3 dimensional lattice types, Bravais lattice. Index system for crystal planes. Simple crystal structures with examples. Reciprocal lattice: diffraction of waves by crystals, Bragg’s law. Reciprocal lattice vectors, Brillouin zones.

2. Band structure:

 Kronig-Penney model and E-k diagram and origin of bandgap. Bloch’s theorem, reduced zone scheme, effective mass approximation, Tight binding model, Fermi levels, Fermi surfaces. Distribution of states in valence and conduction bands, band-filling model: metal, semiconductors and insulators.

3. Phonons

Vibrations of crystals with monoatomic basis, first Brillouin zone, group velocity, two atoms per primitive basis. Quantization of elastic waves, phonon momentum, inelastic scattering by phonons, Raman effect, Phonon heat capacity. Debye and Einstein models for density of states.

4. Magnetic properties of solids

Origin of magnetism; Diamagnetism: quantum theory of atomic diamagnetism; Landau diamagnetism (qualitative discussion); Paramagnetism: quantum theory of paramagnetism; Ferromagnetism: Curie- Weiss law, temperature dependence of saturated magnetisation, Heisenberg's exchange interaction, ferromagnetic domains; Ferrimagnetism and antiferromagnetism; Magnetic resonances.

5. Surface physics

Surfaces and Interfaces: crystallography and electronic structure of surfaces, magnetoresistance in 2-dimensional channel, integral quantized Hall effect, reconstruction and relaxation: 7x7 reconstruction on silicon surface, dislocations, grain boundaries: low angle grain boundaries, triplet grain boundaries.